To reduce the amount of data of multi-channel audio signals with three or more channels, methods of coding audio signals have been developed. Of these, one coding method standardized by the Moving Picture Experts Group (MPEG) is known as the MPEG Surround method. In the MPEG Surround method, 5.1-channel audio signals to be coded, for example, undergo time-frequency conversion and frequency signals resulting from the time-frequency conversion are down-mixed, creating three-channel frequency signals. When the three-channel frequency signals are down-mixed again, frequency signals corresponding to two-channel stereo signals are calculated. The frequency signals corresponding to the stereo signals are coded by the Advanced Audio Coding (AAC) method and Spectral Band Replication (SBR) method. In the MPEG Surround method, spatial information, which indicates spread or localization of sound is calculated at the time when the 5.1-channel signals are down-mixed to the three-channel signals and when the three-channel signals are down-mixed to the two-channel signals, after which the spatial information is coded. Accordingly, in the MPEG Surround method, stereo signals resulting from down-mixing multi-channel audio signals and spatial signal with a relatively small amount of data are coded. Therefore, the MPEG Surround method achieves higher compression efficiency than when a signal in each channel included in a multi-channel audio signal is independently coded.
In the MPEG Surround method, to reduce the amount of information to be coded, three-channel frequency signals are divided into a stereo frequency signal and two channel prediction coefficients, and each divided component is individually coded. The channel prediction coefficients are used to perform predictive coding on a signal in one of three channels according to signals in the remaining two channels. A plurality of channel prediction coefficients are stored in a table, which is a so-called coding book. The coding book is used to improve the efficiency of bits in use. When a coder and a decoder share a common predetermined coding book (or they each have a coding book created by a common method), it becomes possible to transmit more important information with less bits. At the time of decoding, the signal in one of the three channels is replicated according to the channel prediction coefficient described above. Therefore, it is desirable to select a channel prediction coefficient from the coding book at the time of coding.
In a disclosed method of selecting a channel prediction coefficient from the coding book, error defined by a difference between a channel signal before predictive coding and a channel signal resulting from the predictive coding is calculated by using each of all channel prediction coefficients stored in the coding book, and a channel prediction coefficient that minimizes the error in predictive coding is selected. A technology to calculate a channel prediction coefficient that minimizes error by using the least squares method is also disclosed in, for example, Japanese National Publication of International Patent Application No. 2008-517338.